This is an extension of XYZ-Wing that uses four cells instead of three. Each possible value of the hinge cell results in a Z value in one of the cells in the WXYZ-Wing pattern, thus leaving no room for a Z on any cell all four can 'see'.

Its name derives from the four numbers W, X, Y and Z that are required in the hinge. The outer cells in the formation will be Wz, XZ and YZ, Z being the common number

the quote above is from http://www.sudokuwiki.org/WXYZ_Wing and should be amended; Where W is required, but not all of the digits xyz are required within the hinge to function.

see collary located at the bottom of this post.

I have collected the limited data for this technique and have complied a minimal exemplars listing for all the variations I can identify here is this list:

in the above configuration on top of the normal wxyz-wing elimination there may be two restricted commons between sets A&Bwhen this occurs all cells become locked sets and all peer cells for each digit may be eliminated.

the signification difference to note is that group A is comprised within a box as is B, allowing for Two restricted commons {1 per box} and for the elimination it is any cell that sees all Restricted commons between both groups A and B.

i don really see how the cells are overlapped, furthermore it uses 4 digits covering 4 cells which to me is the same concept as a wxyz wing.

this is a copy from a pm i sent regarding the below proposal. i am wondering if some one else could formalize this a bit better to perhaps explain it better or give an alternative view on its function.

i think it has some thing to do with the inherit weak links between the bivalves off the W forming strong links interface linking the two boxes as a locked sets.where y is the restricted common in box 3 and W is the linked restricted common and all shared cells x,z are restricted to the als cells thus all cells seeing xz are removed.

What seems to be the issue here is what defines the term 'wing". Is it how compact the pattern is in terms of the containing houses (which seems to your approach StrmCkr) or the number of strong inferences (or ALS inferences in these examples) employed? Am I right in saying wings only use two ALSs and anything that needs a third one doesn't qualify?

The opening post is concerned with the number of cells involved, but this could be any number if extra passenger digits are added to extend the ALSs.

David, you may prefer chain notation using ALS's, but the history of these patterns supports my interpretation.

In ScanRaid, the term hinge is used where I said vertex.

WXYZ-Wing

This is an extension of XYZ-Wing that uses four cells instead of three. Each possible value of the hinge cell results in a Z value in one of the cells in the WXYZ-Wing pattern, thus leaving no room for a Z on any cell all four can 'see'.Its name derives from the four numbers W, X, Y and Z that are required in the hinge. The outer cells in the formation will be WZ, XZ and YZ, Z being the common number.

daj95376 wrote:David, you may prefer chain notation using ALS's, but the history of these patterns supports my interpretation.

daj95376, that's a strange line of argument! Because early explorers navigated by compass and sextant, would you suggest that we shouldn't be using GPS now?

What I was driving at was; whichever way we look at these things, when does a wing stop being a wing? It appears to me to depend on how many hinges, pivots, or vertices are involved, which is equivalent to how many ALSs there are. The number of cells making up a wing pattern wouldn't then be a factor.

However, the opening post in this thread focuses on patterns restricted to four digits in four cells - which is what StrmCkr's example does.

Danny, whether we use two forcing chains away from a pivot node or a single AIC through it shouldn't matter as we are using exactly the same inferences. What I was asking was simple enough - when does a wing grow too complicated to cease being classed as a wing?

When you wrote:My answer is still a forcing network from a hinge/pivot/vertice cell with short streams -- typically two cells per stream.

You were ducking the question as you haven't defined a clear boundary.

As you don't like using an ALS count to decide, another way of looking at the same thing (I think) would be to say that, apart from the victim cells, all the cells in a wing pattern are confined to two intersecting houses.